{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "#physical constant\n",
    "B_field = 6.\n",
    "EC = 56.1*np.sqrt(B_field)           #in meV (using epsilon=1, the coulomb energy in vacuum)\n",
    "lB = 25.66/np.sqrt(B_field)          #Magnetic length in nm\n",
    "\n",
    "#sample-impurity distance\n",
    "d_si = 0 / lB                  #(above: >0, below: <0)\n",
    "\n",
    "#other distance\n",
    "d_gs = 70. / lB                 #gate-sample distance\n",
    "d_sd = 2.5 / lB                 #sample-detector distance\n",
    "d_gi = d_gs + d_si              #gate to impurity distance\n",
    "d_id = d_sd - d_si              #impurity to detector distance\n",
    "\n",
    "# Dielectric constants\n",
    "beta = np.sqrt(6.6/3.)  #6.6 or 5.33\n",
    "eps  = np.sqrt(6.6*3)\n",
    "\n",
    "broaden = 1.5/EC                  #for clearity of the spectrum\n",
    "energy = np.arange(-40,10.1,0.1) /EC\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#load LL wavefunctoin\n",
    "# These wave function are produced by \n",
    "df_0 = pd.read_csv(r'landau_orbit2_0.csv')\n",
    "df_1 = pd.read_csv(r'landau_orbit2_1.csv')\n",
    "\n",
    "m_total = len(df_0.axes[1])-2\n",
    "\n",
    "prob0 , prob1 = ([] , [])\n",
    "\n",
    "for i in range(m_total):\n",
    "    prob0.append(df_0.iloc[:,2+i].to_numpy())\n",
    "    prob1.append(df_1.iloc[:,2+i].to_numpy())\n",
    "\n",
    "position = np.array(df_0['r_(lB)'])\n",
    "\n",
    "fig , ax = plt.subplots(ncols=2 , figsize = (10,2))\n",
    "for i in range(m_total):\n",
    "    ax[0].plot(position , prob0[i])\n",
    "    ax[1].plot(position , prob1[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Green's function\n",
    "- $G(q) = \\frac{1}{q} \\frac{ sinh(\\beta qd_g)csch(\\beta q(d_g+d_s)) }{1 + \\epsilon coth(\\beta q (d_g + d_s))} $\n",
    "- $d_g$: distance between sample/impurity and gate\n",
    "- $d_s$: distance between sample/impurity and detector\n",
    "\n",
    "    *$G(q=0)=\\frac{d_g\\beta}{\\epsilon}$ $\\newline$\n",
    "    *2D free space: $G(q) = \\frac{2\\pi}{q}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "#q * G(q)\n",
    "q_green = lambda dg,ds,iq: 0 if iq == 0. \\\n",
    "             else 2*np.pi*( np.exp(-1*iq*beta*(ds)) - np.exp( -1*iq*beta*(2*dg+ds) ) ) / (1 + eps - (1-eps) * np.exp( -2*iq*beta*(dg+ds) ))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J0_integral(rV, q, tol=1e-15, d = 1, dr = np.inf, full_output=False):\n",
    "\t\t\"\"\"MPZ: Integrates  Vq = 2 \\\\pi \\\\int_0^\\\\inf  J_0(q r) rV(r) dr.\n",
    "\t\t\t\trV is a callable function, with domain [0, +inf) and range in float.\n",
    "\t\t\t\tq is a float\n",
    "\t\t\t\ttol = Desired absolute error\n",
    "\t\t\t\td = Length scale at which any r-->0 singularities may occur\n",
    "\t\t\t\tdr = Optional; length scale beyond which rV(r) is negligible. Can be important to know when 1 >> dr q\n",
    "\t\t\t\tfull_output is a Boolean: then return number of periods integrated and #func evaluations\n",
    "\n",
    "\t\t\tReturns\n",
    "\t\t\t\tif full_output is False:\n",
    "\t\t\t\t\tVq\n",
    "\t\t\t\tif full_output is True:\n",
    "\t\t\t\t\tVq, number of periods integrated, number of function evaluation\n",
    "\n",
    "\t\t\tExample:\n",
    "\t\t\t\t>>>\tq = 2.\n",
    "\t\t\t\t>>>\tprint mod.mQHfunc.J0_integral(lambda r: np.exp(-r), q)\n",
    "\t\t\t\t>>>\tprint 2 * np.pi / np.sqrt(q**2 + 1)\n",
    "\t\t\t\t\t2.80992589242\n",
    "\t\t\t\t\t2.80992589242\n",
    "\t\n",
    "\t\t\tStrategy:\n",
    "\t\t\t1)\tIntegrate in subintervals [r_j, r_{j+1}], defined by r_j = pi (j + 3/4) / q .\n",
    "\t\t\t\t\tThe r_j's are the approximate zeros of J_0(q r),\n",
    "\t\t\t2)\tTabulate the partial sums, and Euler sum them to accelerate convergence.\n",
    "\t\t\t\t\n",
    "\t\t\t\t\n",
    "\t\t\"\"\"\n",
    "\t\ttwo_pi = 2. * np.pi\n",
    "\t\t\n",
    "\t\tdef euler_sum(S):\n",
    "\t\t\t#Euler summation given partial sums S\n",
    "\t\t\tN = len(S) - 1\n",
    "\t\t\tbinom = [ sp.special.comb(N, n, exact = True) for n in range(N+1) ]\t\t# binomial coef\n",
    "\t\t\treturn np.inner(S, binom) / 2**N\n",
    "\t\t\t#return np.inner(S, sp.stats.binom.pmf(range(N+1),N, 0.5))\n",
    "\t\tdef I(r):\n",
    "\t\t\t#The integrand\n",
    "\t\t\treturn sp.special.j0(q*r)*rV(r)\n",
    "\t\n",
    "\t\tn_Eval = 0\t\t# number of rV() evaluations\n",
    "\t\tn_Quad = 0\n",
    "\t\tstatus = 'converged'\n",
    "\t\tif q==0.:\n",
    "\t\t\t#Break out near singular behaviour near 0\n",
    "\t\t\ta0, abserr, infodict = sp.integrate.quad(rV, 0., d, epsabs=tol/50., full_output = True)[:3]\n",
    "\t\t\tn_Eval+=infodict['neval']\n",
    "\n",
    "\t\t\ta1, abserr, infodict = sp.integrate.quad(rV, d, np.inf, epsabs=tol/50., full_output = True)[:3]\n",
    "\t\t\tn_Eval+=infodict['neval']\n",
    "\t\t\tn_Quad+=2\n",
    "\t\t\tif full_output:\n",
    "\t\t\t\treturn (a0+a1) * two_pi, {'n_quad':n_Quad, 'n_eval':n_eval, 'converged':True}\n",
    "\t\t\telse:\n",
    "\t\t\t\treturn (a0+a1) * two_pi\n",
    "\t\t\t\n",
    "\t\t#Seperate out first interval, [0, r_0], and garauntee subdivision for accuracy\n",
    "\t\tbreak_pt = min(0.375*np.pi/q, d)\n",
    "\t\tif np.pi*0.75/q < dr:\n",
    "\t\t\tbreak_pt = min(0.375*np.pi/q, d)\n",
    "\t\t\ta0, abserr, infodict =  sp.integrate.quad(I, 0., np.pi*0.75/q, epsabs=tol/50., full_output = True, points = [break_pt])[:3]\n",
    "\t\t\tn_Eval+=infodict['neval']\n",
    "\t\t\tn_Quad+=1\n",
    "\t\telse:\n",
    "\t\t\tbreak_pt = min(dr/2., d)\n",
    "\t\t\ta0, abserr, infodict =  sp.integrate.quad(I, 0., dr, epsabs=tol/50., full_output = True, points = [break_pt])[:3]\n",
    "\t\t\tn_Eval+=infodict['neval']\n",
    "\t\t\ta1, abserr, infodict =  sp.integrate.quad(I, dr, np.pi*0.75/q, epsabs=tol/50., full_output = True)[:3]\n",
    "\t\t\tn_Eval+=infodict['neval']\n",
    "\t\t\tn_Quad+=2\n",
    "\t\t\ta0+=a1\n",
    "\t\ta0 *= two_pi\n",
    "\t\t\n",
    "\t\t#Initialize S, ES\n",
    "\t\tr, abserr, infodict = sp.integrate.quad(I, np.pi*0.75/q, np.pi*1.75/q, full_output = True)[:3]\n",
    "\t\tr *= two_pi\n",
    "\t\tn_Eval+=infodict['neval']\n",
    "\t\tn_Quad+=1\n",
    "\t\tS = [r] #partial sums\n",
    "\t\tES = [r] #euler sums\n",
    "\t\t\n",
    "\t\tj = 1.75\n",
    "\t\twhile j < 50:\n",
    "\t\t\tr, abserr, infodict = sp.integrate.quad(I, np.pi*j/q, np.pi*(j+1.)/q, full_output = True)[:3]\n",
    "\t\t\tr *= two_pi\n",
    "\t\t\tn_Eval+=infodict['neval']\n",
    "\t\t\tn_Quad+=1\n",
    "\t\t\tS.append( S[-1] + r )\n",
    "\t\t\t\n",
    "\t\t\tif abs(r) < max(abserr, tol): #Forget Euler summation - absolute convergence!\n",
    "\t\t\t\tif full_output:\n",
    "\t\t\t\t\treturn S[-1] + a0, {'n_quad':n_Quad, 'n_eval':n_eval, 'converged':True}\n",
    "\t\t\t\telse:\n",
    "\t\t\t\t\treturn S[-1] + a0\n",
    "\t\t\tES.append(euler_sum(S))\n",
    "\t\t\n",
    "\t\t\tif\tabs(ES[-1] - ES[-2]) < max(abserr, tol): #Good enough - our work is done.\n",
    "\t\t\t\tif full_output:\n",
    "\t\t\t\t\treturn ES[-1] + a0, {'n_quad':n_Quad, 'n_eval':n_eval, 'converged':True}\n",
    "\t\t\t\treturn ES[-1] + a0\n",
    "\t\t\t\n",
    "\t\t\tj+=1.\n",
    "\t\n",
    "\t\tprint(\"\\tJ0_integral: Poorly behaved integrand!  q = {}, d = {}, tol = {}, n_Quad = {}, n_Eval = {}, \".format(q, d, tol, n_Quad, n_Eval))\n",
    "\t\tprint(\"\\t\\tS - S[-1]:\", np.array(S) - S[-1])\n",
    "\t\tprint(\"\\t\\tES - ES[-1]:\", np.array(ES) - ES[-1])\n",
    "\t\tif full_output:\n",
    "\t\t\treturn ES[-1] + a0, {'n_quad':n_Quad, 'n_eval':n_eval, 'converged':False, 'dS':np.array(S) - S[-1], 'dES':np.array(ES) - ES[-1]}\n",
    "\t\telse:\n",
    "\t\t\treturn ES[-1] + a0\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tJ0_integral: Poorly behaved integrand!  q = 1.68, d = 1, tol = 1e-21, n_Quad = 51, n_Eval = 1134, \n",
      "\t\tS - S[-1]: [ 4.15347023e-01 -1.75231424e-01  7.82494482e-02 -3.60774975e-02\n",
      "  1.69773519e-02 -8.10327295e-03  3.90812062e-03 -1.89989274e-03\n",
      "  9.29427790e-04 -4.56990751e-04  2.25641951e-04 -1.11804895e-04\n",
      "  5.55652398e-05 -2.76864265e-05  1.38263265e-05 -6.91837665e-06\n",
      "  3.46785376e-06 -1.74098166e-06  8.75255461e-07 -4.40578452e-07\n",
      "  2.22028314e-07 -1.12007180e-07  5.65584062e-08 -2.85843524e-08\n",
      "  1.44580465e-08 -7.31836991e-09  3.70697095e-09 -1.87889526e-09\n",
      "  9.52897983e-10 -4.83539431e-10  2.45497622e-10 -1.24701138e-10\n",
      "  6.33733066e-11 -3.22184501e-11  1.63884462e-11 -8.33733083e-12\n",
      "  4.24504876e-12 -2.16027196e-12  1.10156329e-12 -5.59996494e-13\n",
      "  2.86659585e-13 -1.44995127e-13  7.50510765e-14 -3.70814490e-14\n",
      "  2.02060590e-14 -9.10382880e-15  5.77315973e-15 -1.77635684e-15\n",
      "  1.99840144e-15  0.00000000e+00]\n",
      "\t\tES - ES[-1]: [ 4.15347023e-01  1.20057800e-01  3.57834061e-02  1.10404500e-02\n",
      "  3.53658628e-03  1.17790311e-03  4.07797149e-04  1.46473411e-04\n",
      "  5.44114844e-05  2.08249313e-05  8.17926902e-06  3.28439662e-06\n",
      "  1.34389256e-06  5.58746830e-07  2.35499680e-07  1.00428714e-07\n",
      "  4.32652414e-08  1.88052658e-08  8.23802360e-09  3.63405706e-09\n",
      "  1.61312919e-09  7.20091098e-10  3.23086446e-10  1.45634838e-10\n",
      "  6.59263755e-11  2.99604785e-11  1.36648470e-11  6.25366425e-12\n",
      "  2.87059265e-12  1.32160949e-12  6.10178574e-13  2.82218693e-13\n",
      "  1.31006317e-13  6.08402217e-14  2.86437540e-14  1.33226763e-14\n",
      "  6.21724894e-15  2.88657986e-15  1.33226763e-15  6.66133815e-16\n",
      "  2.22044605e-16  6.66133815e-16 -4.44089210e-16  2.22044605e-16\n",
      " -2.22044605e-16  0.00000000e+00  4.44089210e-16  0.00000000e+00\n",
      "  2.22044605e-16  0.00000000e+00]\n",
      "\tJ0_integral: Poorly behaved integrand!  q = 3.21, d = 1, tol = 1e-21, n_Quad = 51, n_Eval = 1092, \n",
      "\t\tS - S[-1]: [ 3.95310963e-01 -2.27679081e-01  1.39054231e-01 -8.77621868e-02\n",
      "  5.65604220e-02 -3.69825154e-02  2.44385670e-02 -1.62802739e-02\n",
      "  1.09146880e-02 -7.35518160e-03  4.97757691e-03 -3.38054089e-03\n",
      "  2.30287517e-03 -1.57283700e-03  1.07667685e-03 -7.38492396e-04\n",
      "  5.07434047e-04 -3.49207353e-04  2.40666319e-04 -1.66063539e-04\n",
      "  1.14727704e-04 -7.93352834e-05  5.49230171e-05 -3.80467718e-05\n",
      "  2.63868117e-05 -1.83045651e-05  1.27160699e-05 -8.83011508e-06\n",
      "  6.14473416e-06 -4.26905045e-06  2.97684811e-06 -2.06742354e-06\n",
      "  1.44586359e-06 -1.00221524e-06  7.04348083e-07 -4.85781649e-07\n",
      "  3.44511725e-07 -2.34950919e-07  1.69595009e-07 -1.12926339e-07\n",
      "  8.44380642e-08 -5.34777519e-08  4.29231374e-08 -2.44775242e-08\n",
      "  2.26590742e-08 -1.03139229e-08  1.27567455e-08 -3.38904249e-09\n",
      "  7.91286192e-09  0.00000000e+00]\n",
      "\t\tES - ES[-1]: [ 3.95310960e-01  8.38159378e-02  1.97517546e-02  5.20927488e-03\n",
      "  1.52697787e-03  4.89234007e-04  1.68059374e-04  6.08666584e-05\n",
      "  2.29474195e-05  8.92422959e-06  3.55709987e-06  1.44646189e-06\n",
      "  5.98039531e-07  2.50754768e-07  1.06413826e-07  4.56338954e-08\n",
      "  1.97496658e-08  8.61699256e-09  3.78697840e-09  1.67512970e-09\n",
      "  7.45328799e-10  3.33391981e-10  1.49853019e-10  6.76552148e-11\n",
      "  3.06696890e-11  1.39555034e-11  6.37201403e-12  2.91888735e-12\n",
      "  1.34103839e-12  6.17950136e-13  2.85327317e-13  1.32005518e-13\n",
      "  6.12843110e-14  2.84217094e-14  1.32116540e-14  6.10622664e-15\n",
      "  2.77555756e-15  1.33226763e-15  6.66133815e-16  3.33066907e-16\n",
      "  0.00000000e+00  1.11022302e-16 -2.22044605e-16 -1.11022302e-16\n",
      "  0.00000000e+00 -2.22044605e-16 -1.11022302e-16  0.00000000e+00\n",
      " -1.11022302e-16  0.00000000e+00]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12f8148f0>]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#\\n_{impurity}(q)\n",
    "n_q_imp = -1\n",
    "\n",
    "#q* G(q)_{impurity}\n",
    "q_green_imp = lambda iq: q_green(d_gi,d_id,iq)\n",
    "\n",
    "#q * \\phi_{impurity}(q)\n",
    "q_phi_q_imp = lambda iq: n_q_imp * q_green_imp(iq)\n",
    "\n",
    "# \\phi_impurity(r)\n",
    "phi_r_imp = np.array([J0_integral(q_phi_q_imp, ir,tol=1e-21, d = 1,\\\n",
    "                                  dr = np.inf,full_output=False) for ir in position]) / (2*np.pi)**(2)\n",
    "\n",
    "# impurity potential if defect is in isotropic environment\n",
    "phi_r_imp_iso = -1/(position[:]**2+d_id**2)**0.5 / (1+eps)\n",
    "\n",
    "plt.plot( position , phi_r_imp*EC )\n",
    "plt.plot( position , phi_r_imp_iso*EC )\n",
    "# plt.plot(position,prob0[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E0:  [-22.77607139 -13.5547264  -10.07150909  -8.21209738  -7.02600017\n",
      "  -6.18809872  -5.55577886  -5.05489625  -4.64123657  -4.2848544 ]\n",
      "E1:  [-18.1653989  -14.68218158 -10.76560884  -8.62902051  -7.30344097\n",
      "  -6.38589275  -5.69964934  -5.15334664  -4.69215551  -4.27980688]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta = position[1]-position[0]\n",
    "potential_bare = phi_r_imp\n",
    "\n",
    "E0=[]\n",
    "E1=[]\n",
    "for i in range(m_total):\n",
    "    E0.append( np.sum( prob0[i] * potential_bare * position *2*np.pi * delta) )\n",
    "    E1.append( np.sum( prob1[i] * potential_bare * position *2*np.pi * delta) )\n",
    "\n",
    "spectrum0 = np.zeros((len(position),len(energy)))\n",
    "spectrum1 = spectrum0[:]\n",
    "\n",
    "for i in range(m_total):\n",
    "    energy_spread =  1/(broaden * (2*np.pi)**0.5)*np.exp( -((energy-E0[i]) / (broaden) )**2/2 )\n",
    "    spectrum0 = spectrum0 + np.array([energy_spread]) * np.array([prob0[i]]).transpose()\n",
    "    energy_spread =  1/(broaden * (2*np.pi)**0.5)*np.exp( -((energy-E1[i]) / (broaden) )**2/2 )\n",
    "    spectrum1 = spectrum1 + np.array([energy_spread]) * np.array([prob1[i]]).transpose()\n",
    "\n",
    "fig, ax = plt.subplots(nrows=1,ncols=2)\n",
    "ax[0].imshow(np.rot90(spectrum0),extent =[position.min()*lB, position.max()*lB, energy.min()*EC, energy.max()*EC], aspect='auto')\n",
    "ax[1].imshow(np.rot90(spectrum1),extent =[position.min()*lB, position.max()*lB, energy.min()*EC, energy.max()*EC], aspect='auto')\n",
    "\n",
    "print('E0: ',np.array(E0)*EC)\n",
    "print('E1: ',np.array(E1)*EC)\n",
    "\n",
    "\n",
    "ax[0].plot( position*lB , phi_r_imp*EC )\n",
    "ax[1].plot( position*lB , phi_r_imp*EC )\n",
    "\n",
    "np.savetxt(r'result_simZLL.csv' , spectrum0)\n",
    "np.savetxt(r'result_simPotential.csv' , phi_r_imp)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Princeton",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
